Here's how to make those characters used in spelling and to show pronunciation of Elvish Words (+ a few other interesting letters you may or may not need):

Press and hold down the ALT key while typing the four number code on your NUMPAD, then release ALT.
(On some laptops without a separate number pad on the keyboard you will need to press the ALT+FN keys together while typing the number code)

On most computers with Windows, you can click on Start then All Programs then System Tools then Character Map. This brings up a handy tool for finding all those odd and assorted characters not usually found on a standard American keyboard. You can select the character you want, copy it, and insert it into your document, post, etc.
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From Bêthberry:

Want some help writing some inspired Sindarin or Khazdul? Looking for some Black Speech to lend a bit of colour to your orc characterization? Try these links.